Apparatus and method for low complexity combinatorial coding of signals
View Patent ↗The invention utilizes low complexity estimates of complex functions to perform combinatorial coding of signal vectors. The invention disregards the accuracy of such functions as long as certain sufficient properties are maintained. The invention in turn may reduce computational complexity of certain coding and decoding operations by two orders of magnitude or more for a given signal vector input.
1. A method for combinatorial coding and decoding, the method comprising the steps of:
receiving a vector comprising speech, audio, image, or video;
receiving a value n based on a number of positions in the vector;
receiving a value d based on a number of occupied positions within the vector;
generating a value F′(n,d) based on a logarithmic approximation of the combinatorial function of F(n,d) and comprising generating a logarithmic approximation of a numerator of F(n,d) and generating a logarithmic approximation of a denominator by subtracting a combinatorial function Q′(d) from the numerator; and
using the value F′(n,d) to code or decode the vector to produce coded or decoded speech, audio, image, or video, wherein the step generating of the value F′(n,d) comprises the step of generating a value F′(n,d)=R′(k), where R′(k) is an approximation of the function a k , and where a is a logarithm base,
wherein the step of generating a value F′(n,d)=R′(k) further comprises the steps of:
generating an integer component k i and a fractional component k f , based on a value k such that k=k i +k f ;
generating a value K f , wherein K f is based on a low resolution Talyor series expansion of 2 k f ;
producing the value R′(k) based on K f .
2. The method of claim 1 wherein Q′(d) is an approximation of the function Q(d)=Σ j=1 d log a (j), where a is a logarithm base.
3. The method of claim 1 wherein
Q
′
(
d
)
=
∑
j
=
2
d
2
-
l
(
j
)
⌊
2
l
(
j
)
log
2
(
j
)
-
1
⌋
,
where l(j) is a shift factor.
4. The method of claim 3 wherein the summation is generated as
Q
′
(
d
)
=
∑
j
=
2
d
2
-
l
(
j
)
⌊
2
l
(
j
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log
2
(
j
)
-
1
⌋
,
where l(j) is a shift factor.
5. The method of claim 1 wherein the step of producing the value R′(k) based on K f further comprises generating:
R ′( k )=└2 k i −l └2 l K f ┘┘.
6. The method of claim 1 wherein the value F′(n,d) such that
F
′
(
n
,
d
)
>
n
!
d
!
(
n
-
d
)
!
and F′(n,d)>F′(n−1,d)+F′(n−1,d−1).
7. The method of claim 1 wherein the approximation of the function a k is obtained using a Taylor series expansion method.
8. An apparatus comprising:
a vector generator receiving a vector comprising speech, audio, image, or video;
a combinatorial function generator receiving a value n based on a number of positions in the vector, receiving a value d based on a number of occupied positions within the vector, and generating a value F′(n,d) based on a logarithmic approximation of the combinatorial function of F(n,d) and comprising generating a logarithmic approximation of a numerator of F(n,d) and generating a logarithmic approximation of a denominator by subtracting a combinatorial function Q′(d) from the numerator; and
a coder/decoder using the value F′(n,d) to code or decode the vector to produce coded or decoded speech, audio, image, or video,
said combinatorial function generator generating of the value F′(n,d) including generating a value F′(n,d)=R′(k), where R′(k) is an approximation of the function a k , and where a is a logarithm base, generating an integer component k i and a fractional component k f , based on a value k such that k=k i +k f ; generating a value K f , wherein K f is based on a low resolution Talyor series expansion of 2 k f , and producing the value R′(k) based on K f .
9. The apparatus of claim 8 wherein Q′(d) is an approximation of the function Q(d)=Σ j=1 d log a (j) where a is a logarithm base.
10. The apparatus of claim 8 wherein
Q
′
(
d
)
=
∑
j
=
2
d
2
-
l
(
j
)
⌊
2
l
(
j
)
log
2
(
j
)
-
1
⌋
,
where l(j) is a shift factor.